In a longitudinal wave, the individual disturbances that
make up the wave are in the same direction as the wave itself.
Examples of a longitudinal wave are a Slinky and sound. A
longitudinal wave is in contrast to a transverse wave. In a
transverse wave, the individual disturbances that make up the wave
are perpendicular to the direction of the wave itself. A good
example of a transverse wave is a wave on a rope.

2. How will the frequency of the sound used for echolocation
affect the size of objects that can be detected? Will higher or lower
frequencies allow for detection of smaller objects with
echolocation?

The wavelength of a wave determines how it will be
reflected. The shorter wavelengths of higher frequencies mean that
the echolocation of bats and dolphins help them identify more
detail -- or smaller objects -- than would be possible with longer
wavelengths or lower frequencies.

3. To the good ear of a careful listener, a difference can be
heard when the same violin string is plucked at different locations.
Why would this be?

Plucking a string in different places will excite
different amounts of different kinds of standing waves. So a
careful listener will, indeed, be able to tell a difference.

4. As a scale is played on a piano, from low to high, the pitch
or frequency of the sound increases. What happens to the
wavelength?

speed = frequency x wavelength

As the frequency increases, the wavelength decreases. That
means that higher frequencies correspond to shorter
wavelengths.

5. For strings of the same length and tension, why would a
heavier, thicker guitar string produce a lower pitch than a lighter,
thinner one?

Experimentally, we will find that the velocity of a wave on a string
is related to the tension in the string T and the linear mass density
(mass per unit length) by

v2 = T /

or

So a larger linear mass density
will give a smaller value for v, the speed of the wave on the string. The
wavelength of the standing wave is determined by the length of the string.
So a smaller value for v, the speed of the wave on the string, means the frequency
will be smaller (or lower) since

wave speed = wavelength x frequency

Another way to think of this is just to think that the greater
mass will respond more slowly simply due to Newton's Second Law of
Motion,

F = m a

so a more massive string will produce a lower frequency.

6. In terms of standing waves, explain why long organ pipes
produce sound of lower pitch than short pipes.

7. In a good audio system, why is the low-frequency speaker
(the woofer) much larger than the high-frequency speaker
(tweeter)?

Low-frequency sound waves have a l-o-n-g wavelength and
l-o-n-g wavelength waves are produced more efficiently with a
larger speaker. Larger speakers have more mass so their resonant
frequency is lower.

8. If a guitar string is very lightly touched at its mid-point,
the pitch heard will shift to an octave higher. Explain why.

Lightly touching a guitar string at its mid-point will
stop the vibration of the fundamental frequency (and other
harmonics) that has an antinode there. It will not
affect the next higher harmonic that has a node at the
center. This next higher harmonic has a wavelength of one-half
that of the harmonic; that means its pitch is twice as high
as the fundamental frequency -- and that is an octave higher.

10. Why is the speed of sound so much greater in liquids and
solids than in air?

Molecules that compose a liquid or a solid are held in
place far more strongly than the molecules that compose air (or
any gas). Any disturbance of a molecule in a liquid or solid means
that molecule is pulled back to its equilibrium position (and then
coasts on beyond that) far faster than for a molecule in a gas.

11. Why will the temperature in a concert hall affect the pitch
of the instruments?

wave speed = frequency x wavelength

Wave speed depends upon temperature so the frequency and
wavelength of the standing waves that produce the sound in an
instrument also depend upon temperature. A band that is tuned
inside a nice warm building will soon be out of tune as they march
into a cold open, outdoor stadium.

12. Why do you see lightning before you hear the thunder it
produces?

The speed of light is very great (3.0 x 108
m/s). It is far, far greater than the speed of sound (about 345
m/s). If you see distant lightning, the light arrives at your eye
immediately but it requires about four minutes for the sound to
travel a mile.

14. What is the same when you hear a high C played on a French
horn and a high C played on a piano?

The fundamental frequency -- the lowest frequency heard
-- is the same for both instruments.

15. Why does a high C played on a French horn sound different
from a high C played on a piano?

The two instruments have a different set of
harmonics -- also called overtones -- which gives each instrument
its distinctive "voice" or quality or timbre.

16. How many octaves are there on a standard piano
keyboard?

A standard piano keyboard has 88 keys and there are 12
keys to an octave.

N = 88 / 12 = 7.3 octaves

20. Suppose you stand at an intersection and listen to an
ambulance as it approaches you and then goes away from you. Explain
what you will hear.

As the ambulance approaches, you hear its siren with a
pitch that is higher than if it were standing still. As it
goes away from you, you hear its siren with a pitch that is
lower than if it were standing still. This is an example of
the Doppler Effect.

22. Supersonic flights that are restricted over land are
allowed over the ocean. Does this mean there is no pressure wave--or
sonic boom--created over the ocean?

There is still a sonic boom over the ocean. But there are
far fewer people to be disturbed than on land.

Typical Multiple Choice
Questions:

1. Light and sound are both waves. You can see a ringing bell
inside an evacuated glass container but you can not hear it. This is
because

A) of resonance

B) light travels faster than sound

C) sound requires air to be transmitted and light does not

D) light passes through glass but sound does not

2. Sound is

A) an electromagnetic wave

B) a polarized wave

C) a transverse wave

D) a longitudinal wave

3. "Supersonic" means

A) lower than the range of human hearing

B) higher than the range of human hearing

C) faster than the speed of sound

D) slower than the speed of sound

4. "Ultrasonic" means

A) lower than the range of human hearing

B) higher than the range of human hearing

C) faster than the speed of sound

D) slower than the speed of sound

5. "Infrasonic" means

A) lower than the range of human hearing

B) higher than the range of human hearing

C) faster than the speed of sound

D) slower than the speed of sound

6. Bats and dolphins use echolocation to navigate or the find food
or to find their way without relying on sight. The frequencies they
use are

A) supersonic

B) infrasonic

C) ultrasonic

D) microsonic

7. If you double the frequency of a sound wave, you also double
its

A) wavelength

B) speed

C) amplitude

D) all of the above

8. The range of human hearing is about

A) 10 Hz to 100 Hz

B) 50 Hz to 500 Hz

C) 50 Hz to 20 000 Hz

D) 1 000 Hz to 100 000 Hz

9. Sound travels fastest in

A) air (a gas)

B) water (a liquid)

C) steel (a solid)

D) vacuum

10. The speed of sound in air depends upon

A) wavelength

B) frequency

C) temperature

D) amplitude

11. Increasing the length of a vibrating string will

A) decrease its resonance frequency

B) decrease its amplitude

C) increase its amplitude

D) increase its resonance frequency

12. Ella Fitzgerald made commercials for Memorex in which she used
her voice to break a wine glass. This is an example of

A) echolocation

B) reflected sound

C) ultrasonic frequencies

D) resonance

13. Beats are heard when two sounds have

A) nearly the same amplitude

B) nearly the same frequencies

C) twice the amplitude

D) exactly twice the wavelength

14. The fundamental frequency present in a sound is the

A) sum of all the frequencies mixed together

B) difference between the highest and lowest frequencies
present

C) lowest frequency present

D) highest frequency present

15. The "pitch" of a sound is determined by its

A) overtones frequencies

B) harmonics frequencies

C) fundamental frequency

D) resonance frequencies

16. The quality or timbre -- the distincitive characteristic -- of
a sound is determined by its

A) overtones or harmonics

B) amplitude or loudness

C) attack or decay

D) fundamental frequency

17. You hear beats with a frequency of 3
Hz when you strike a tuning fork that vibrates at 256 Hz
and a chime. The chime has a frequency of

A) 3 x 256 Hz = 768 Hz

B) 259 Hz

C) (256 / 3) Hz = 85.3 Hz

D) 250 Hz

18. The fundamental frequency of a violin string is
440 hertz. The frequency of its
second harmonic is

A) 110 Hz

B) 220 Hz

C) 440 Hz

D) 880 Hz

19. Consider a musical note of 440
hertz ("concert 'A'").
Two octaves higher is represented
by a musical note of

A) 220 Hz

B) 880 Hz

C) 1320 Hz

D) 1760 Hz

20. The intensity or loudness of a musical sound is related to the
sound wave's

A) wavelength

B) frequency

C) amplitude

D) wave speed

21. Suppose you play a note of a certain pitch on a violin. You
can produce a lower-pitched note
by

A) shortening the length of the string that is allowed to
vibrate

B) increasing the tension of the string

C) decreasing the linear mass density of the string

D) lengthening the part of the string that vibrates.

Answers to these Typical Multiple Choice
Questions:

1. Light and sound are both waves. You can see a ringing bell
inside an evacuated glass container but you can not hear it. This is
because

A) of resonance

B) light travels faster than sound

C) sound requires air to be
transmitted and light does not

D) light passes through glass but sound does not

2. Sound is

A) an electromagnetic wave

light is an
electromagnetic wave

radio and television and X-rays
are also electromagnetic waves

B) a polarized wave

only transverse
waves can be polarized

longitudinal waves can not be
polarized

C) a transverse wave

D) a longitudinal wave

3. "Supersonic" means

A) lower than the range of human hearing

B) higher than the range of human hearing

C) faster than the speed of
sound

D) slower than the speed of sound

4. "Ultrasonic" means

A) lower than the range of human hearing

B) higher than the range of human
hearing

Rangefinders on
Polaroid cameras use ultrasound.

Ultrasound is used for medical
imaging.

Bats and dolphins use ultrasound
for echolocation.

C) faster than the speed of sound

D) slower than the speed of sound

5. "Infrasonic" means

A) lower than the range of human
hearing

B) higher than the range of human hearing

C) faster than the speed of sound

D) slower than the speed of sound

6. Bats and dolphins use echolocation to navigate or the find food
or to find their way without relying on sight. The frequencies they
use are

A) supersonic

B) infrasonic

C) ultrasonic

Both bats and
dolphins use ultrasound with frequencies of about 50 kHz and
above.

D) microsonic

7. If you double the frequency of a sound wave, you also double
its

A) wavelength; doubling the
frequency means you reduce the wavelength to one-half

B) speed; changing the frequency
should have no effect on the speed.

C) amplitude ; changing the frequency
should have no effect on the amplitude.

D) all of the above

E) none of the above

8. The range of human hearing is about

A) 10 Hz to 100 Hz

B) 50 Hz to 500 Hz

C) 50 Hz to 20 000 Hz

D) 1 000 Hz to 100 000 Hz

9. Sound travels fastest in

A) air (a gas)

B) water (a liquid)

C) steel (a solid)

The
inter-molecular forces that hold a molecule in place in a
solid are much stronger than those in a liquid or a gas so
they move the molecule more rapidly -- just like a mass
attached to a stronger spring. This more rapid movement of
the molecules means that sound is transmitted faster
too.

D) vacuum

10. The speed of sound in air depends upon

A) wavelength

B) frequency

C) temperature

D) amplitude

11. Increasing the length of a vibrating string will

A) decrease its resonance
frequency

Increasing the
length of the string means the wavelength of the standing
wave is also increased. And increase in wavelength means a
decrease in the frequency.

B) decrease its amplitude

C) increase its amplitude

D) increase its resonance frequency

12. Ella Fitzgerald made commercials for Memorex in which she used
her voice to break a wine glass. This is an example of

A) echolocation

B) reflected sound

C) ultrasonic frequencies

D) resonance

13. Beats are heard when two sounds have

A) nearly the same amplitude

B) nearly the same
frequencies

C) twice the amplitude

D) exactly twice the wavelength

14. The fundamental frequency present in a sound is the

A) sum of all the frequencies mixed together

B) difference between the highest and lowest frequencies
present

C) lowest frequency
present

D) highest frequency present

15. The "pitch" of a sound is determined by its

A) overtones frequencies

B) harmonics frequencies

C) fundamental
frequency

D) resonance frequencies

16. The quality or timbre -- the distincitive characteristic -- of
a sound is determined by its

A) overtones or
harmonics

B) amplitude or loudness

C) attack or decay

D) fundamental frequency

17. You hear beats with a frequency of 3
Hz when you strike a tuning fork that vibrates at 256 Hz
and a chime. The chime has a frequency of

A) 3 x 256 Hz = 768 Hz

B) 259 Hz

fbeat
= difference in frequencies = f2 - f1
= 3 Hz

3 Hz = f2 - 256
Hz

f2 = 259
Hz

C) (256 / 3) Hz = 85.3 Hz

D) 250 Hz

18. The fundamental frequency of a violin string is
440 hertz. The frequency of its
second harmonic is

A) 110 Hz

B) 220 Hz

C) 440 Hz

D) 880 Hz

19. Consider a musical note of 440
hertz ("concert 'A'").
Two octaves higher is represented
by a musical note of

A) 220 Hz; this is one octave
lower.

B) 880 Hz ; this is one octave
higher.

C) 1320 Hz

D) 1760 Hz

One octave above
A at 440 Hz is twice that frequency, 880 Hz.

One octave above that A at 880
Hz is 1760 Hz.

20. The intensity or loudness of a musical sound is related to the
sound wave's

A) wavelength

B) frequency

C) amplitude

D) wave speed

21. Suppose you play a note of a certain pitch on a violin. You
can produce a lower-pitched note
by